Feature Request: Search filter block for block theme templates

### Impacted plugin

Search

### What

On block themes like TT3 there is no widget area for the search template, so it is not possible to use Jetpack Search without Instant Search.

### How

With the work-around described on https://wordpress.org/support/topic/inline-search-and-fse-block-theme/#post-16360491 (creating a custom widget area and a shortcode to render it in a block template) it is possible to use a block template for Jetpack Search without Instant Search.

A dedicated block for the Search/Filter widget would be better :)

Start by reviewing the Search/Filter widget and the block-template workaround described in the linked WordPress support thread. Define how a dedicated block should work in a block theme's search template, then verify that it can provide Jetpack Search without Instant Search.

Written by the indexing model from the issue text.